PostgreSQL provides triggers and rule systems to automatically perform a certain function when an event such as INSERT, UPDATE, or DELETE is performed. Triggers and rules cannot be defined on SELECT statements, except for _RETURN, which is used in the internal implementation of PostgreSQL views.
From a functionality point of view, the trigger system is more generic; it can be used to implement complex actions more easily than rules. However, both trigger and rule systems can be used to implement the same functionality in several cases. From the performance point of view, rules tend to be faster than triggers, but triggers tend to be simpler and more compatible with other RDBMs, since the rule system is a PostgreSQL extension.